After arithmetic, the typical order of classes (The ones I took, and the one I believe most often taught in American schools) goes like this:

Algebra Geometry More Advanced Algebra Trigonometry Calculus

I don't have any book recommendations and I don't know of any books that would cover all those topics. There are many books on algebra however, and I don't think it will particularly matter which one you use. It should get you up to speed very quickly.

The other topics are probably less important for intro CS. I don't think I ever used calculus or trig for any CS classes. Very basic geometry might be used as examples.